1. Field
The present invention generally relates to the field of logarithmic amplifiers and detectors.
2. Background
Logarithmic amplifiers are useful wherever a signal of large dynamic range must be reduced to one of substantially smaller dynamic range, and where equal ratios in the input domain must be transformed to equal increments in the output domain. In communications and instrumentation applications, this has the value that the output represents the input expressed in decibel form.
Equation 1 represents the general transfer characteristic of a logarithmic amplifier.
                              V          out                =                              V            0                    ⁢                      log            ⁡                          (                                                V                  in                                                  V                  z                                            )                                                          (        1        )            In this equation, V0 represents the slope and Vz represents the intercept voltage (i.e., the input voltage for which the output voltage is zero). This is, of course, a highly non-linear conversion, with consequences which may be unexpected if the peculiar nature of the log transformation is not kept clearly in mind. Thus, while an attenuator inserted in front of a linear amplifier would change the slope at the output, it would not affect the slope of the output of a log-amp; similarly, an offset voltage at the output of a linear amplifier has no relevance to the amplitude of an AC signal, while an offset added to the output of a log-amp alters the apparent magnitude of its input.
It should be appreciated that the accuracy of a logarithmic amplifier relies heavily on the stabilization of the parameters V0 (slope) and Vz (intercept). Slope can be made stable over process by means of accurate design. In bipolar technology, the intercept is commonly proportional to absolute temperature (PTAT). As a consequence, it is more difficult to stabilize over process and temperature by accurate design, and generates the amplifier temperature error:
                              V                      out            ,            error                          =                              -                          V              0                                ⁢                      log            ⁡                          (                              T                                  T                  0                                            )                                                          (        2        )            For the temperature range of −50 C<T<100 C this is equivalent to an input error of −2.5 dB<input reference error<2 dB. The relationship described in Equation 2 holds for LOG-amplifiers and detectors implemented with bipolar transistors. For CMOS or other technologies, different relations may hold. Regardless, the key problem with the intercept is still the same: the intercept is generally temperature dependent and sensitive to device mismatch/offset, frequency dependencies of the amplifiers, etc.
Previous attempts have been made to correct the temperature dependent intercept voltage. One approach has been to utilize input correction to make Vin PTAT. This has been implemented through, by way of examples, a resistive divider with a PTAT transfer or an amplifier with a PTAT transfer. Circuits employing this approach were capable of making the log conformance temperature independent, but these circuits also needed to cope with the full bandwidth of the circuit.
Yet another approach has dealt with output compensation (e.g., adding a correction voltage or current at the output of the log-amp). However, this approach is not exact and results in a temperature dependent log-conformance error. Furthermore, the correction voltage/current is dependent on log
      (          T              T        0              )    ,and accurate compensation requires the LOG-slope to be accurately known. In practice, this parameter is also subject to small part-to-part variations (and variations over other operating conditions as temperature, frequency, etc.).
Thus, prior approaches to the problem of logarithmic amplifier intercept stabilization have not produced an overall technique that is applicable irrespective of the structure and error contributions in the individual sections.